We apply the hyperboloid membrane limit to the general Kerr-AdS metrics and
their recently studied super-entropic cousins and obtain a new class of
rotating black holes, for which the rotational parameters in multiple
directions attain their maximal value---equal to the AdS radius. These new
solutions have a potential application in the description of holographic fluids
with vorticity. They also possess interesting thermodynamic properties: we show
that---despite the absence of Misner strings---the Bekenstein--Hawking
entropy/area law is still violated, raising a question about the origin of this
violation.
